High School Math Problems

This Logic Puzzle For High School Kids In Singapore Is Going Viral. Can You Solve It?

This weekend a TV host in Singapore posted a simple logic/math question designed for 14- and 15-year-old students in that country. It runs like this:

If you can't make out the writing in the image above, here is the problem, complete with the original errors:

Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15 May 16 May 19June 17 June 18 July 14 July 16August 14 August 15 August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.Bernard: At first I don't know when Cheryl's birthday is, but I know now.Albert: Then I also know when Cheryl's birthday is.

When is Cheryl's birthday?

Go on, try and figure it out. We've posted the result (and the solution) at the bottom of the page.

Remember, Singapore routinely scores at or near the top of math rankings worldwide, and this riddle is actually aimed at kids in the top 40% of their grade. So while you should feel dumber than a 14-year-old Singapore math student if you can't solve it, that's not necessarily that damning a statement. At least, we hope it isn't: Three AskMen editors failed to solve it (admittedly, we only spent a couple of minutes on it); we wrote out the solution below based on what other, cleverer people on the internet found out.

Solution

Albert only knows the month of Cheryl's birthday, not the date, while Bernard knows the date of her birthday, but not the month, of Cheryl's birthday. The secret here is the two "unique" days, May 19 and June 18 — none of the other days are numbered 18 or 19.

1. According to Bernard's admission, Albert can be absolutely sure that Bernard doesn't know the exact date. That rules out May and June, because if it was in either May or June, it's conceivable that Bernard would know the exact date if he was given 18 or 19 as the day of her birthday, because then he would immediately know that it was either May 19 or June 18. But Albert knows Bernard doesn't know the date for sure, so it has to be in July or August. That leaves five potential days:

July 14 July 16August 14 August 15 August 17

2. Bernard then says "At first I don't know when Cheryl's birthday is, but I know now." That means he couldn't have been given 14th as the day, because in this scenario he wouldn't be able to tell whether it was July 14 or August 14. So it has to one of three remaining days.

July 16August 15 August 17

3. Albert then says "Then I also know when Cheryl's birthday is." Remember, Albert only knows the month. But from Bernard's comment he can narrow it down to those three dates we listed above. However, if he had been told "August," he still wouldn't be able to know the date with absolute certainty, as it could be either August 15 or 17. However he does know the date with certainty, so it had to be July 16.